Subgroups — #22624903

Order 9344.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989484	C₂	1	1	yes	maximal, characteristic
2	#17989455	C₂	1	1	yes	maximal, characteristic
3	#17988842	C₂	1	1	yes	maximal, characteristic
4	#14556670	—	2	1	no	—
5	#14556665	—	2	1	no	—
6	C₂×#11924011	C₂²	1	1	yes	characteristic
7	#14556567	—	2	1	no	—
8	#14556523	C₄	1	1	yes	characteristic, complemented
9	#14556515	—	2	1	no	—
10	C₂×Q₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#64408	—	4	1	no	—
12	C₂²⋊#64408	—	4	1	no	—
13	C₄×#64408	—	2	2	no	—
14	#11924031	—	4	1	no	—
15	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
16	#11924011	—	4	1	no	—
17	C₂×#10596831	D₄	1	1	yes	characteristic
18	C₄⋊Dic₇₃	—	2	1	no	—
19	#11924007	—	4	1	no	—
20	#11924005	—	4	1	no	—
21	C₂×Q₈×C₇₃	—	2	1	no	—
22	Q₁₆×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₇₃	D₈	1	1	yes	characteristic
25	C₂×#64408	—	4	2	no	—
26	Q₈×C₇₃	—	4	1	no	—
27	Q₈×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₇₃	—	4	1	no	—
31	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
32	C₄×D₇₃	—	2	1	no	—
33	C₄×D₇₃	—	2	1	no	—
34	C₈×C₇₃	—	2	1	no	—
35	#10596831	—	2	1	no	—
36	C₂²×C₇₃	#102	1	1	yes	characteristic
37	C₂×D₇₃	—	2	1	no	—
38	C₂×D₇₃	—	4	1	no	—
39	#64408	—	8	2	no	—
40	C₄×C₇₃	—	8	1	no	—
41	C₄×C₇₃	#99	1	1	yes	characteristic
42	C₄×C₇₃	#104	1	1	yes	characteristic
43	Dic₇₃	—	2	1	no	—
44	Dic₇₃	—	8	1	no	—
45	C₂×C₇₃	—	2	1	no	—
46	C₂×C₇₃	#327	1	1	yes	characteristic
47	D₇₃	—	4	1	no	—
48	#1340	—	73	1	no	maximal, Sylow
49	C₇₃	#1340	1	1	yes	characteristic, complemented, Sylow
50	#470	—	73	1	no	—
51	#349	—	73	1	no	—
52	H(3,ℤ/4)	—	73	1	no	—
53	C₂×Q₁₆	#64408	1	1	yes	characteristic, complemented
54	C₂×M₁₆	—	73	1	no	—
55	C₂²⋊Q₈	—	146	1	no	—
56	#117	—	146	1	no	—
57	M₃₂	—	146	1	no	—
58	#106	—	73	1	no	—
59	#103	—	146	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	—	73	1	no	—
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	292	1	no	—
64	C₂×C₈	—	73	1	no	—
65	C₂×C₈	C₂×#64408	1	1	yes	characteristic
66	C₄⋊C₄	—	292	1	no	—
67	C₄⋊C₄	—	292	1	no	—
68	C₄⋊C₄	—	146	1	no	—
69	C₂²⋊C₄	—	292	1	no	—
70	C₂²⋊C₄	—	292	1	no	—
71	C₄²	—	146	2	no	—
72	C₁₆	—	292	1	no	—
73	C₂³	—	73	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	292	2	no	—
78	C₂×C₄	—	292	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	146	1	no	—
81	C₂×C₄	—	146	1	no	—
82	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	146	1	no	—
85	C₂²	—	292	1	no	—
86	C₂²	—	146	1	no	—
87	C₂²	#14556653	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	584	1	no	—
90	C₄	—	584	2	no	—
91	C₄	—	146	1	no	—
92	C₄	#14556649	1	1	yes	characteristic
93	C₄	#14556655	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	292	1	no	—
96	C₂	#17989438	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989438
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×Q₁₆×C₇₃	C₄
socle	C₂×C₇₃	#327
hypercenter	C₂×Q₁₆	#64408
hypocenter	C₇₃	#1340
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
8. #14556523	C₄	semidirect
10. C₂×Q₁₆×C₇₃	C₄	semidirect
49. C₇₃	#1340	semidirect
53. C₂×Q₁₆	#64408	semidirect